Yes, developers jobs are well paid in London, depending on the company, there are several places that take advantage of their developers and pay poorly. My advice to most London devs is move company often until you find a salary you're happy with, companies need you more than you need the company.

I would go even further and say it's easier now for non-EU people, because we just eliminated a whole class of advantaged competition. Now when you compete with someone from the EU you're on equal terms.

Everyone always talks about London, but misses out some of the other cities/large towns.

Manchester maybe a better option than London. Manchester is cheaper and has almost all the things you want from London without a lot of the negatives. Pay isn't nearly as good but the costs of living in Manchester are about 1/2 to 1/3rd of what London is.

If you want better weather the south-coast has Bournemouth (lots of smaller to mid-sized companies that do web development and insurance).